Related papers: Gerberto e la Geografia Tolemaica
Gerbert of Aurillac was the most prominent personality of the tenth century: astronomer, organ builder and music theoretician, mathematician, philosopher, and finally pope with the name of Silvester II (999-1003). Gerbert introduced firstly…
We have found an empirical law for the variation of the length of the Earth's day with geologic time employing Wells's data. We attribute the lengthening of the Earth's day to the present cosmic expansion of the Universe. The prediction of…
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
We present a modern reconstruction of the classical formula, first derived by medieval Arab astronomers, that describes the trajectory of the tip of a gnomon's shadow during the day as a function of latitude, solar declination, and gnomon…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
We show that the arrow of time is intimately related to the geometry and topology of the whole universe, and is therefore best understood as a cosmological phenomenon.
We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical…
Classical clocks measure proper time along their worldline, and Riemannian geometry provides tools for predicting the time shown by clocks in both flat and curved spacetimes. Common approaches to time in quantum systems, based for instance…
Examples of cyclic (periodic) behavior in geophysical data abound. In many cases the primary period is known, such as in daily measurements of rain, temperature, and sea level. However, many time series of measurements contain cycles of…
We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
The geoid is the true physical figure of the Earth, a particular equipotential surface of the gravity field of the Earth that accounts for the effect of all subsurface density variations. Its shape approximates best (in the sense of least…
Calendars are broadly used in society to display temporal information, and events. This paper describes a new R package with functionality to organize and display temporal data, collected on sub-daily resolution, into a calendar layout. The…
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…
The possibility of an increasing gravitational constant $G$ and its implication on the Earth's history are discussed. The model is consistent with geophysical and astronomical data. The number of days in early epochs predicted by the model…
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
An enquiry into the physical nature of time and space and into the ontology of quantum mechanics from a metageometric perspective, resulting from the belief that geometric thought and language are powerless to farther understanding of these…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…